Cross-correlation matrix: Difference between revisions

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Revision as of 21:15, 27 October 2006

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For [[stochastic process]]es, including those that arise in [[statistical mechanics]] and Euclidean [[quantum field theory]], a '''correlation function''' is the [[correlation]] between [[random variable]]s at two different points in space or time. If one considers the correlation function between random variables at the same point but at two different times then one refers to this as the '''autocorrelation function'''. If there are multiple random variables in the problem then correlation functions of the ''same'' random variable are also sometimes called autocorrelation. The autocorrelation can be intuitively understood as an indicator of how the random variable at a given point changes with time. Correlation functions of different random variables are sometimes called '''cross correlations'''. Cross correlations are a useful indicator of the dependencies among different random variables as a function of time.

Correlation functions used in [[correlation function (astronomy)|astronomy]], [[financial analysis]], [[quantum field theory]] and [[statistical mechanics]] differ only in the particular stochastic processes they are applied to with the caveat that we are dealing with "quantum distributions" in QFT.